Mesh reconstruction using tracking data
There is currently no way to reconstruct a more detailed mesh between the camera-solved Control Points from within blender. Thats because the Camera Solver does not look at the image data at all, It only deals with the marker positions. The Control Point-Tracker is the one who finds commonality between frames. So you could just add more Control Points, but you'll of course never get a z-value for every pixel of the frame.

So I see this two ways of achieving, what I think you want:

Manual Scene Reconstruction - this works well with rectangular scenes like rooms, hallways, roads, houses

Blender Movie Clip Editor offers a few basic tools for scene orientation after camera solution: automatic origin, floor or wall plane setup from selected tracks. With this you can line up Blenders coordinate-grid with rectangular objects in the movie clip. In a camera-viewport with the movie-clip enabled as background its easy now to manually reconstruct rectangular objects via extrude on the axes x,y or z. Also, the BLAM Blender addon may be helpful with this process. It also features camera solution from one single image instead of a movie clip.
In the end you can texture the mesh using the UV-projection modifier to project the movie onto the mesh.

Foto Series Reconstruction Workflow - also works with non-rectangular scenes and objects, like reliefs, uneven terrain

Extract ca. 25 frames with significant parallax from your clip (e.g. take every 10th frame), then...

Option A:
Use the free 123D Catch-App from Autodesk to generate the model and export it to Blender.

Option B:
Follow this video tutorial, which describes the workflow of reconstructing and texturing a mesh from a series of fotos using the free programs VisualSFM and Meshlab, and exporting the model to Blender.
VisualSFM is used to reconstruct a 3d-point-cloud from a series of fotos, with Meshlab you approximate a mesh from the points and optionally create a UV-Map with projected parts of the fotos as texture. From there the model can be exported to Blender.